What is the derivative of (x^3+1)^5 ?

The derivative of (x^3+1)^5 is 15x^2(x^3+1)^4

What is the first derivative of (x^3+1)^5 ?

The first derivative of (x^3+1)^5 is 15x^2(x^3+1)^4

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derivative of

(x^{3} + 1)^{5}

15 x^{2} (x^{3} + 1)^{4}

Solution steps

\frac{d}{d x} ((x^{3} + 1)^{5})

Apply the chain rule:

5 (x^{3} + 1)^{4} \frac{d}{d x} (x^{3} + 1)

= 5 (x^{3} + 1)^{4} \frac{d}{d x} (x^{3} + 1)

\frac{d}{d x} (x^{3} + 1) = 3 x^{2}

= 5 (x^{3} + 1)^{4} \cdot 3 x^{2}

Simplify

= 15 x^{2} (x^{3} + 1)^{4}

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What is the derivative of (x^3+1)^5 ?
The derivative of (x^3+1)^5 is 15x^2(x^3+1)^4
What is the first derivative of (x^3+1)^5 ?
The first derivative of (x^3+1)^5 is 15x^2(x^3+1)^4